Magnetoconvection in Dependence on Roberts Number

Marginal instabilities in a horizontal unstably stratified rapidly rotating fluid layer permeated by an azimuthal magnetic field growing linearly with distance from the vertical rotation axis, are investigated in dependence on electromagnetic boundary conditions and Roberts number . Electrical conductivities of perfectly thermally conducting boundaries are either infinite or finite Earthlike ones. Following Soward's (1979) results the case of gives the instabilities of MAC-waves with much greater frequencies than for the case of q 1. Critical frequencies of MAC waves are most sensitive on Roberts number for q 1 and lose this sensitivity for q2. On the other hand the critical Rayleigh numbers are slightly dependent on q 1. Many qualitative differences in the dependences on q do exist for infinitely and finitely conducting boundaries. The former do not allow fast eastward modes for q 1 and the latter, e.g. allow eastward MC-waves with azimuthal wave number m = 1. The MC-waves are almost independent on Roberts number q.     

Analysis of State of Stress During The 1997 Earthquake Swarm In Western Bohemia

Focal mechanisms of 70 events of the January 1997 earthquake swarm were analysed using the Gephart and Forsyth method to determine the state of stress in the West Bohemia/Vogtland region and to reveal possible stress variations during the swarm activity. The method was applied to the whole set of 70 focal mechanisms and to several subsets distinguishing magnitudes of events and the spatial and temporal distribution of the swarm. The three representative stress models A ( ₁ ,A: 0/45 (az/dip), ₂ A: 134/35, ₃ A: 243/25), B ( ₁ ,B: 162/38, ₂ B: 263/14, ₃ B: 10/49), and C ( ₁ C: 135/30, ₂ C: 1/50, ₃ C: 239/23) which could characterise the state of stress in the region were found. Model C can be considered to be the most probable stress model because of its consistency with the European stress field. The results of the stress analysis applied to the individual subsets of focal mechanisms indicate that the state of stress was more uniform during the first phase of the swarm. To distinguish between the fault plane and the auxiliary plane of fault plane solutions a statistical approach was used. The results showed that the fault planes striking NW-SE and dipping 45° to NE were activated during the swarm.     

The derivatives of the lunar disturbing potential harmonics with respect to euler's angles

Summary The derivatives of the harmonicsP _n ^(k) (sin _O)cos kT_O andP _n ^(k) (sin _O)sin kT_O, occurring in the development of the lunar disturbing potential, are derived upto n=4 and for k== 0, 1, ..., n. The equatorial co-ordinates _OT_O are referred to the Moon's mass centre; the procedure for the solar disturbing potential is formally identical.     

(ϖμ/ϖT) P of the lower mantle

We estimate (/T) _P of the lower mantle at seismic frequencies using two distinct approaches by combining ambient laboratory measurements on lower mantle minerals with seismic data. In the first approach, an upper bound is estimated for |(/T) _P | by comparing the shear modulus () profile of PREM with laboratory room-temperature data of extrapolated to high pressures. The second approach employs a seismic tomography constraint ( lnV _S / lnV _P ) _P =1.8–2, which directly relates (/T) _P with (K _S /T) _P . An average (K _S /T) _P can be obtained by comparing the well-established room-temperature compression data for lower mantle minerals with theK _S profile of PREM along several possible adiabats. Both (K _S /T) and (/T) depend on silicon content [or (Mg+Fe)/Sil of the model. For various compositions, the two approaches predict rather distinct (/T) _P vs. (K _S /T) _P curves, which intersect at a composition similar to pyrolite with (/T) _P =–0.02 to –0.035 and (K _S /T) _P =–0.015 to –0.020 GPa/K. The pure perovskite model, on the other hand, yields grossly inconsistent results using the two approaches. We conclude that both vertical and lateral variations in seismic velocities are consistent with variation due to pressure, temperature, and phase transformations of a uniform composition. Additional physical properties of a pyrolite lower mantle are further predicted. Lateral temperature variations are predicted to be about 100–250 K, and the ratio of ( lnp/ lnV _S ) _P around 0.13 and 0.26. All of these parameters increase slightly with depth if the ratio of ( lnV _S / lnV _P ) _P remains constant throughout the lower mantle. These predicted values are in excellent agreement with geodynamic analyses, in which the ratios ( ln / lnV _S ) _P and ( / lnV _S ) _P are free parameters arbitrarily adjusted to fit the tomography and geoid data.     

The effect of the velocity of the centre of a cyclone on the generation of microseisms

Summary The influence of the velocity of the movement of the centre of the cycloneV _c.c. on the rate of amplitudes' change A/t and periods' change T/t of storm microseisms is investigated. The dependence A/t=k V _c.c. and T/t=k ¹ V _c.c. is obtained. Unmovable depression (V _c.c. =0) does not stipulate the change of A/t and T/t.

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u V _c.c. A/t T/t . A/t=k V _c.c. T/t=¹ V _c.c. . (V _c.c. =0) A/t T/t.

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Presented as a scientific communication to the IASPEI Assembly in Madrid, Sept. 1969.     

Friction constitutive law with rate and state dependences

A general formula for the Dieterich-Ruina friction constitutive law with rate and state (n-state variables,n=1, 2,...) dependences has been obtained and discussed under the assumption that the slip acceleration a varies ion a linearly with the slip displacement , namelya = a ₀ + (-₀). Wherea ₀, ₀ are initial constants, is the acceleration rate and constant.a ₀ and may be arbitrary constants (positive, negative or zero).The extreme value of frictional resistance and the existence condition of the extreme value, which are very important and govern to some degree the motion process of a frictionally slipping mechanical system, have been analyzed. A critical value _c which is the measure of the velocity weakening and velocity strengthening of the mechanical system, and its properties and the relationship to the extreme problem have been studied. Again, according to the critical value _c, the concepts of light or strong velocity weakening (or strengthening) are introduced.A possibly new phenomenon that frictional resistance may vary in some kind of decayed oscillation is found. Finally, the condition for the smallest frictional resistance for a slipping mechanical system with nonuniform acceleration has been obtained.     

Relevant Magnetic Parameters and Heavy Metals from Relatively Polluted Stream Sediments - Vertical and Longitudinal Distribution Along a Cross-City Stream in Buenos Aires Province,Argentina

Previous magnetic and geochemical studies of stream sediments in the Northeast of Buenos Aires Province, in the Greater La Plata area, have revealed a high level of trace elements, especially lead and zinc. Continuing these preliminary works, new sampling sites were considered in order to improve and increase the magnetic mapping of this area. This part of the study focuses especially on the magnetic properties of sediments from a cross-city stream. Such stream receives a variable pollutant load from urban, industrial and diffuse sources.Concentration-dependent magnetic parameters, magnetic carriers (para, anti and ferrimagnetic) and their features (e.g. softer or harder magnetic carrier, grain size distribution, etc.) have been calculated using magnetic measurements. According to magnetic parameters and heavy metal loads two main distinctive groups of sediment-cores are distinguished. The vertical distribution of sediments reveals a recent anthropogenic influence, possibly, belonging to the last 20-40 years.Four out of all the magnetic parameters (magnetic susceptibility, anhysteric remanent magnetisation, S-ratio and _ARM/) were chosen in order to investigate their relationship with contents of heavy metals. In all the cases, good positive correlations were obtained using linear regression. However, more significant correlation factors were achieved for grain size and magnetic feature-dependent parameters ( _ARM/ and S-ratio) than for magnetic concentration-dependent parameters. Therefore, the _ARM/ and the S-ratio seem to be the most relevant magnetic parameters to describe the vertical and longitudinal distribution of heavy metals present in these stream sediments. The non-significant relationship between heavy metals and concentration-dependent parameters could be explained taking into account the discrimination of the two distinctive groups. The group belonging to the Coastal Plain shows a clear linear trend between heavy metals and magnetic susceptibility and anhysteric remanent magnetisation.     

The intensity of the main phase of geomagnetic storms in relation to the parameters of the solar wind

Summary On the basis of investigating 10 storms (1965–1967) good correlation was found between the density of the solar wind energy (₂=1/2mNv²) and the intensity of the main phase of the geomagnetic storms, expressed in terms of the maximum decrease of the horizontal intensity (B=H/cos). The relation between ₂, or Nv², and B could then be used to determine the quantities and ₀ ( is the factor expressing the increase in energy density in the magnetosphere, ₀ is the energy density of the particles in a quiet magnetosphere). A comparison with the directly observed distribution of the energy density of the particles in the magnetosphere indicates that the computed value of ₀ seems to be realistic. The magnitude of the factor will have to be checked again.     

A note on the stress-dilatancy relation for simulated fault gouge

Theoretical constraints on the stress-dilation relation for a deforming Coulomb material requirev ifC=0 andv sin^-1( _m / _m ) always, wherev is the dilation angle, is the friction angle,C is cohesion, _m is the maximum shear stress, and _m is the mean effective stress. Recent laboratory measurements of friction and dilatancy of simulated fault gouge show that small amplitude shear-load cycling causes compaction and consolidation. Comparison of the data with theory indicates that such load cycling produces: (1) increased coefficient of friction (or friction angle), (2) increased cohesion, and (3) increased dilatancy rate (or dilation angle). Under certain conditions of load cycling without significant plastic shear strain accumulation ( ^p <0.005) we find thatv exceeds both and, in contrast to theory, sin^-1( _m / _m ). This result is interpreted in terms of enhanced cohesion and overconsolidation, which lead to residual stresses within the gouge. An analogy is drawn between these special loading conditions and those extant on natural faults. In particular, our results imply that jostling and minor stress variations associated with microearthquakes may produce strengthening of fault gouge and changes in the fault zone's stress-dilatancy relation. Hence, compaction associated with microseismicity may lead to subsequent dilation of fault gouge, even for faults with large displacement rates and large net offsets (e.g., San Andreas). In regions where such dilation persists over sufficient displacements (on the order of the critical slip distance for seismic faulting) it may tend to inhibit unstable slip.     

The gross features of the lithosphere-asthenosphere system in Europe from seismic surface waves and body waves

Long-period recordings of dispersive Rayleigh waves along numerous station lines, or profiles, in Europe have for the first time permitted a uniform inversion of these observations based on a new method of phase velocity regionalization.Regional dispersion relations obtained by this method have then been subjected to a complete inversion procedure commonly known as the hedgehog method. The results are presented in a map outlining the thickness of the lower lithosphere (lid) and the shear (S) velocities in both the lid and the asthenosphere channel.A comparison of these results with the minimum compressional (P) wave velocities in the asthenosphere and their corresponding depths provides an estimate of theV _p /V _s ratio for the asthenosphere in the European area.Contribution No. 314, Institute of Geophysics, ETH-Zürich, Switzerland.     

Seismic risk of circum-Pacific earthquakes: II. Extreme values using Gumbel's third distribution and the relationship with strain energy release

In a previous paper (Makropoulos andBurton, 1983) the seismic risk of the circum-Pacific belt was examined using a whole process technique reduced to three representative parameters related to the physical release of strain energy, these are:M ₁, the annual modal magnitude determined using the Gutenberg-Richter relationship;M ₂, the magnitude equivalent to the total strain energy release rate per annum, andM ₃, the upper bound magnitude equivalent to the maximum strain energy release in a region.The risk analysis is extended here using the part process statistical model of Gumbel's IIIrd asymptotic distribution of extreme values. The circum-Pacific is chosen being a complete earthquake data set, and the stability postulate on which asymptotic distributions of extremes are deduced to give similar results to those obtained from whole process or exact distributions of extremes is successfully checked. Additionally, when Gumbel III asymptotic distribution curve fitting is compared with Gumbel I using reduced chi-squared it is seen to be preferable in all cases and it also allows extensions to an upper-bounded range of magnitude occurrences. Examining the regional seismicity generates several seismic risk results, for example, the annual mode for all regions is greater thanm(1)=7.0, with the maximum being in the Japan, Kurile, Kamchatka region atm(1)=7.6. Overall, the most hazardous areas are situated in this northwestern region and also diagonally opposite in the southeastern circum-Pacific. Relationships are established between the Gumbel III parameters and quantitiesm ₁(1),X ₂ and , quantities notionally similar toM ₁,M ₂ andM ₃ although is shown to be systematically larger thanM; thereby giving a physical link through strain energy release to seismic risk statistics. Inall regions of the circum-Pacific similar results are obtained forM ₁,M ₂ andM ₃ and the notionally corresponding statistical quantitiesm ₁(1),X ₂ and , demonstrating that the relationships obtained are valid over a wide range of seismotectonic enviroments.     

Coulomb constitutive laws for friction: Contrasts in frictional behavior for distributed and localized shear

We describe slip-rate dependent friction laws based on the Coulomb failure criteria. Frictional rate dependence is attributed to a rate dependence of cohesionc and friction angle . We show that differences in the stress states developed during sliding result in different Coulomb friction laws for distributed shear within a thick gouge layer versus localized shear within a narrow shear band or between bare rock surfaces. For shear within gouge, shear strength is given by =c cos + _n sin, whereas for shear between bare rock surfaces the shear strength is =c cos + _n tan, where and _n are shear and normal stress, respectively. In the context of rate-dependent Coulomb friction laws, these differences mean that for a given material and rate dependence of the Coulomb parameters, pervasive shear may exhibit velocity strengthening frictional behavior while localized shear exhibits velocity weakening behavior. We derive from experimental data the slip-rate dependence and evolution ofc and for distributed and localized shear. The data show a positive rate dependence for distributed shear and a negative rate dependence for localized shear, indicating that the rate dependence ofc and are not the same for distributed and localized shear, even after accounting for differences in stress state. Our analysis is consistent with the well-known association of instability with shear localization in simulated fault gouge and the observation that bare rock surfaces exhibit predominantly velocity weakening frictional behavior whereas simulated fault gouge exhibits velocity strengthening followed by a transition to velocity weakening with increasing displacement. Natural faults also exhibit displacement dependent frictional behavior and thus the results may prove useful in understanding the seismic evolution of faulting.     

Analysis of aeromagnetic anomalies over the central part of the Narmada-Son lineament

The Narmada-Son lineament (NSL) forms a major tectonic feature on the Indian subcontinent. The importance of this lineament lies in its evolution as well as its tectonic history. The lineament seems to have been active since Precambrian times. In order to understand the history of its evolution, it is necessary to know what igenous activity has been taking place along this lineament, and how the Deccan trap volcanics, which cover large areas along this lineament, have erupted.For the study of this problem an analysis of the aeromagnetic anomaly map lying between 76°15 to 77°30E and 21°45 to 22°50N has been carried out. Four different profiles (B ₁ B ₁,B ₂ B ₂,B ₃ B ₃ andB ₄ B ₄) have been drawn in N-S direction over this area and interpreted in terms of the intrusive bodies present within or below the surface of Deccan trap exposures. Inversion and forward modelling techniques have been adopted for interpretation purposes. An analysis of frequency spectra along the profiles has also been carried out to estimate the average depth of the different magnetic bodies. These results have been correlated with the available geological information. It has been found that most of the small wavelength anomalies are caused by dyke-like bodies within or below the Deccan trap at a depth of less than 0.5 km.     

Estimation of the Source Time Function Based on Blind Deconvolution with Gaussian Mixtures

It is demonstrated that the blind deconvolution method is fully capable of recovering the unknown Greens function and of estimating the source time functions from observed seismic data of small earthquakes. Based on the assumption of the Gaussian-mixture model of the Greens function, the newly-formulated algorithm is evaluated using synthetic seismic data along with those of the May 8, 1996 Mexico earthquake (M_c = 4.6). Since the estimated results closely match the theoretical input very well, the method is then employed to analyze the source time functions of the July 7, 1995 Pu-Li, Taiwan earthquake (M_L = 5.3). The stations triggered by this event were azimuthally well covered. Using the estimated source time functions, information pertaining to the directivity effect is readily obtained, and the actual fault plane of this event is identified, thus clearly indicating that this method provides a most efficient way to estimate the source time function of a small earthquake.Acknowledgment The authors would like to express their thanks to two anonymous reviewers for their valuable suggestions and Dr. I. Santamarias courteous assistance. They also appreciate the efforts of Drs. H.C. Chiu and R.J. Rau, who provided the seismic data and the fault plane solutions. The National Science Council, Taiwan, has supported this research (NSC 91-2119-M-194-011).     

Elektronenproduktion,Rekombination, Elektronendichte und Absorption in der ionosphärischenD-Region und ihre jahreszeitlichen Variationen

Zusammenfassung Es wird die Gleichung für die Elektronenproduktionq(z) abgeleitet, die die meteorologischen Elemente der Mesosphäre berücksichtigt. Nach Angaben über die mit Satelliten und Raketen gemessene Röntgenstrahlung mit 8 Å wird das Differentialspektrum des ionisierenden Energieflusses für eine mittlere Sonnenaktivität konstruiert. Auf dieser Grundlage und nach der bekannten Intensität der Strahlung Ly- sowie nach Angaben über dieElektronenproduktion der kosmischen Strahlung werden die Profileq _Rö(z),q _Ly-(z) undq _CR(z) für mittlere geographische Breiten und Standardatmosphäre entwickelt. Nach eingehender Analyse der vollständigen Gleichung für den effektiven Rekombinationskoeffizienten wird für die Verhältnisse in der tiefen Ionosphäre der Beitrag jeder einzelnen Komponente der Gleichung bestimmt. ist eine recht veränderliche Grösse, die von den aeronomischen und meteorologischen Verhältnissen und der Sonnenzenitdistanz abhängt. Aus den fürq(z) und (z) erhaltenen Angaben werden zwei ElektronendichteprofileN(z) für =30° und 75° erhalten. Das ProfilN(z) bei =30° wird mit dem gemittelten Profil einer umfangreichen Gruppe experimentell gefundener VerteilungenN(z) verglichen; das Profil bei =75° wird durch Messung der deviativen und nondeviativen Absorption für eine längere Zeitperiode überprüft. In beiden Fällen hat sich die Richtigkeit der theoretisch erhaltenen Profile bestätigt. Die jahreszeitlichen Variationen der nondeviativen Absorption in derD-Region sind ausschliesslich durch die Variationen der meteorologischen Parameter im Bereich der Mesopause bei konstantem Energiefluss der ionisierenden Strahlung bedingt.

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Summary An equation about the electron production is deduced in which the meteorological elements of the mesosphere are taken into account. The differential spectrum of the ionizing energy flux with 3 Å for average solar activity is constructed on evidence from rocket and satelitc measurements. The profilesq _Rö(z),q _Ly-(z) andq _CR(z) for mean geographical latitudes and standard atmosphere are plotted on that basis as well as on data fot the known intensity of the Ly- emission and the electron production of the cosmic rays. An exhaustive analysis is made of the full equation for the effective recombination coefficient and the contribution of all its components at lower ionosphere conditions is determined. is a rather variable quantity, dependent on the aeronomical and meteorological condition of the area under consideration, as well as on the solar zenith angle. Two profiles for the electron concentrationN(z) at =30° and 75° are drawn on the basis of data forq(z) and (z). The profileN(z) at =30° is compared with the averaged profile of a large group experimentally obtained distributionsN(z); the profile at =75° is checked by measurements of the deviative and nondeviative absorption taken for a lengthy period. Both checks are in good agreement with the theoretically obtained profiles. The seasonal variations of the nondeviative absorption in theD region could be completely explained with the variations of the meteorological parameters in the mesopause area at constant energy flux of the ionizing radiation.

     

Self-affine growth pattern of earthquake rupture zones

Data from 41 moderate and large earthquakes have been used to derive a scaling law for fault parameters. Fault lengthL, widthW and areaS are empirically related byLS andWS where 0.6<<0.7, 0.3<<0.4 and +=1. These relations indicate that the growth pattern of earthquake rupture zones is statistically self-affine. It is also found that these relations are similar to the relation derived from a diffusion-limited aggregation (DLA) model with anisotropic sticking probability. This suggests that a modified DLA model could describe the evolution of earthquake rupture zones.     

Relation between the field of surface heat flow and the distribution ofP n -wave velocities for continents

Summary The dependence between P_n-wave velocities and the surface heat flow, temperature at the core-mantl boundary and thickness of the Earth's crust for continents (Europe, Asia, North America and Australia) was investigated statistically in connection with the problem of lateral inhomogeneities in the upper mantle. The relations obtained were compared with those determined under laboratory conditions. The conclusion is that temperature and pressure effects may provide additional explanations of the regional variations of P_n-wave velocities observed in most continents.

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auum ¶rt;auu mu n¶rt; a nmu uua(P_n ), nm mn nm, mnam a u m mum a u¶rt;aa u n uuuma ¶rt;¶rt;m mu P_n. nua ¶rt;a mama aam u¶rt;au nu m n¶rt; amuu u u ¶rt;au u mnam a¶rt;um mmmuu mamau n¶rt;aa am. am ¶rt;, m ua uu m P_n- ¶rt; amu muma n¶rt;m auu m¶rt;uauu u a nmu muua.

     

Water uptake and equilibrium sizes of aerosol particles at high relative humidities: Their dependence on the composition of the water-soluble material

Equilibrium water uptake and the sizes of atmospheric aerosol particles have for the first time been determined for high relative humidities, i.e., for humidities above 95 percent, as a function of the particles chemical composition. For that purpose a new treatment of the osmotic coefficient has been developed and experimentally confirmed. It is shown that the equilibrium water uptake and the equilibrium sizes of atmospheric aerosol particles at large relative humidities are significantly dependent on their chemical composition.List of symbols A proportionality factor - a _w activity of water in a solution - c _{p v} specific heat of water vapour at constant pressure - c _w specific heat of liquid water - f relative humidity - l _w specific heat of evaporation of water - M _i molar mass of solute speciesi - M _s mean molar mass of all the solute species in a solution - M _w molar mass of water - m ₀ mass of an aerosol particle in dry state - m _i mass of solute speciesi - m _s mass of solute - m _w mass of water taken up by an aerosol particle in equilibrium state - m total molality=number of mols of solute species in 1000 g of water - m _i molality of solute speciesi - m _k total molality of a pure electrolytek - O(m ²) remaining terms being of the second and of higher powers ofm - p ⁺ standard pressure - p total pressure of the gas phase - p pressure within a droplet - p ₁,p ₂,p ₃ coefficients in the expansion of M - p _1i, p_2i, p_3i specific parameters of ioni - p _s saturation vapour pressure - p _w water vapour pressure - R _w individual gas constant of water - r radius of a droplet - r ₀ equivalent volume radius of an aerosol particle in dry state - T temperature - T ₀ standard temperature - T ₁ temperature of the pure water drop in the osmometer - v _w specific volume of pure water - z _i valence of ioni - _i relativenumber concentration of ioni in a solution - correction term due to the adsorption of ions at liquid-solid interfaces - activity coefficient of solute speciesi in a solution, related to molalities - I bridge current - T temperature difference between solution and pure water drop in the osmometer - exponential mass increase coefficient - _w specific chemical potential of water vapour - _w specific chemical potential of water - ⁰ _w specific chemical potential of pure water vapour - ⁰ _w specific chemical potential of pure water - ₀ density of an aerosol particle in dry state - _w density of pure water - surface tension of a droplet - ₀ surface tension of pure water, i.e., at infinite dilution of the solute - osmotic coefficient - _k osmotic coefficient of a solution of a pure electrolytek - _k osmotic coefficient of a solution of a mixed solute - _M fugacity coefficient of water vapour - ^s _{i=1 i} z ² _i This work is part of a Ph.D. thesis carried out at the Meteorological Institute of the Johannes Gutenberg-Universität, Mainz.     

Effects of the interplanetary magnetic field sector structure in the winter ionosphere

Summary The ionospheric effects of the interplanetary magnetic field (IMF) sector boundary crossings are studied for the winters of 1963–69. They are considerably stronger for proton than for non-proton sector boundaries. There are two different types of effects. The geomagnetic type is a disturbance, observed in geomagnetic activity, the night-time ionosphere and the day-time F2 region near the geomagnetic equator. The effect in the ionosphere is interpreted in terms of the IMF sector boundary crossing related changes in geomagnetic activity. The tropospheric type is aquietening, observed in tropospheric vorticity and in the day-time mid-and low-latitude ionosphere (except the geomagnetic equator region). The mechanism of this effect remains unexplained.

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¶rt;m u m nu mau nam aum n () ¶rt; u 1963–69. u m u ¶rt; nm ¶rt; a mau. mm ¶rt;a m¶rt; muna m. aum m u, a¶rt;a aum amumu, u u ¶rt; F2 amu uuaum ama. mu u m ¶rt;mu uu aum amumu, m a nu mau . n mun m nu, a¶rt; aumu mn u ¶rt; ¶rt;- u uum u (a uu amuaum ama). au m ma um.

     

On reflection and diffraction of pressure waves from floating ice

Summary The diffraction of a pressure wave arising from the edge of the floating ice due to an incident wave of the formH[t–(xcos/)+ (ysin/)], whereH(t) is the Heaviside step function, has been studied. The ice sheet has been taken to be moving with a velocity much less than the velocity of sound in the liquid. The problem has been solved using an approximate method of solving Wiener Hopf problems. Finally, the pressure field at a large distance from the edge has been derived in a closed form evaluating the integrals by the saddle point method.